German leaders warned Thursday that they could not rule out shutting Germany's borders with its neighbor countries because of troublingly high coronavirus infections fuelled by more contagious variants in countries like Austria and the Czech Republic.

"We believe it would be sensible to declare both (Austria and Czech Republic) as mutation areas. This will likely happen," said Bavarian state premier Markus Soeder.

He had warned late Wednesday that if the Czech Republic was unable to take appropriate measures to curb contagion, then a "border closure must also be an issue."

Germany in late January banned most travelers from countries classed as so-called mutation areas or places hardest hit by new, more contagious coronavirus variants.

Only a handful of exceptions are allowed to enter Germany from these countries, including returning Germans and essential workers.

With neighboring EU countries continuing to report high infection numbers in part fuelled by variants, German leaders fear that keeping the borders open could compromise the country's efforts to curb contagion.

Baden-Wuerttemberg state premier Winfried Kretschmann said in a regional parliament session that if virus variants were to keep propagating in neighboring countries, then "of course that can in the extreme case also lead to border closures."

Austria has already ordered restrictions to stop people from leaving the mountainous Tyrol region, which Chancellor Sebastian Kurz says has been hit by the biggest outbreak in Europe of the South African variant.

Anyone leaving the region must now show a negative coronavirus test, with fines of up to 1,450 euros ($1,750) for anyone who fails to comply.

But Soeder, whose region borders Tyrol, said he feared that "a second Ischgl" was in the making – referring to the Austrian ski region which became a coronavirus superspreader hotspot early on in the pandemic.

Tyrol "is not taking the development seriously," he said.

Meanwhile, Saxony state, which lies next to the Czech Republic, said it was imposing tougher checks from Saturday with restrictions to also affect cross-border workers.

Only workers in essential sectors – such as doctors or employees in elderly care homes – would be allowed to travel in.

But they would be required to take virus tests daily and commit to traveling only between their homes and workplaces.

The Czech government said Thursday it would block off three hard-hit districts, including two on the German border, stopping people living in these zones from leaving and others from entering.

Czech public health officials want the curb to be in force for three weeks, although there are likely to be exceptions.

Despite measures taken in the country, two right-wing lawmakers this week caused an uproar for refusing to wear masks in the Czech Parliament.